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Math Help - f(x) = x^x domain/range

  1. #1
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    f(x) = x^x domain/range

    f(x) = x^x

    So I think the domain would include:

    a) all x where x > 0
    b) all rational x where x < 0 and the denominator is odd (negative integers and fractions with odd denominators)
    c) 0, if you define 0^0 to be 1 or 0. My two calculators give different answers for this.

    But would it include negative irrational numbers? Would it include some and not others? Would there be a difference between algebraic and transcendental numbers?
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  2. #2
    MHF Contributor
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    Re: f(x) = x^x domain/range

    Hey euphony.

    One question you need to ask is whether you want to include complex numbers as part of your range or co-domain of your function.

    If you include complex numbers then things become a lot easier to define.
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